A method of accurately rendering algebraically defined shapes that can be
used to render alignment targets, or for other purposes, is disclosed. The
method can render shapes as a bitmap image for machine vision alignment
training, for computer display for human observation, and for computer
printout for documentation. The method can aid in rendering targets on the
objects to be located by providing input to a computer-aided design (CAD)
system, or by directly controlling devices such as laser engravers. The
rendering method is fast, extremely accurate, and can handle substantially
arbitrary shapes. Targets are defined by a real-valued function of
position in the real plane that gives the distance from that position to
the nearest point on a target boundary. The function gives distance as a
positive value for points inside the figure, and as a negative value for
points outside the figure. An edge model is used to map distance to
real-valued image intensity. By choosing appropriate edge model
parameters, edge sharpness, focus, video gain, and noise can be modeled.